Interval criteria for oscillation of certain matrix differential systems

Abstract

By employing a generalized Riccati technique and an averaging technique, interval oscillation criteria are established for the second order matrix differential system of the form [ P( t) Y′]′+ Q( t) Y=0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of [ t 0,∞), rather than on the whole half-line. Our results are presented in the form of a high degree of generality, handle the cases which are not covered by known criteria and can be applied to extreme cases such as lim t→∞λ 1[∫ t 0 tQ(s) ds]=−∞ . In particular, several interesting examples that dwell upon the importance of our results are included.